Equivalence Relations and Partitions

[@goodplacetostop2973]

8:18 Find someone who loves you as much as Michael loves the floor function. 17:46 Good Place To Stop

[@jairusmartinez1209]

just came across this video for a discrete math class i am taking- super helpful btw!. i could not help but notice your build- i had a feeling like you were a hiker, cyclist, or rock climber and sure enough, you are an OG rock climber. thanks for the math content and keep shreddin out there man

[@jamesyeung3286]

Thanks! I've been looking for a video on this for some time

[@sapientum8]

3:36 it's amazing how Michael can erase the board with just one tap. Mathematical superpowers ?

[@jimallysonnevado3973]

For the converse, just say xRy if and only if they are in the same partition and prove that indeed it is an equivalence relation.

[@pauljackson3491]

I'm posting this before I swatch because it is a meta-question. How come on this video, the other equ-video, and some others the video is smaller than usual? The similar videos on the right take up almost half the the screen - left/right - while the are normally about a quarter.

[@matekon2]

Thank you!

[@natepolidoro4565]

Great video

[@davidseed2939]

It would help me to give an example before the generality. It help me visualize. Eg the domain is complex numbers the equivalence relation is the norm ie r when z=r.exp(i.theta). So [z] is a circle radius r centred at the origin of the argand diagram.

[@noahtaul]

2:25 Why not just take x in [x]=[y]? Then you’re done.

[@tomatrix7525]

I think technically speaking your solution is perfect, since xRx is true, but he may want to give a proof that gives more of an intuition as to why. Not sure though, good observation

[@trueriver1950]

Hi: I seem to have missed "The previous video". It's here, for anyone else who missed it and wants to catch up: kzbin.info/www/bejne/hWelcoSDqtOViM0 And while I am here I will also suggest that whenever you have a follow on video is helpful to post the link in the description; and to post a forward link in the description of the previous one. Warmly :)

[@MichaelPennMath]

I have a student intern adding these links as we speak!

[@Icenri]

Not all heroes wear capes

[@trueriver1950]

@@MichaelPennMath appreciated :)

[@dae8105]

Yooo

[@Happy_Abe]

What if A is the empty set? Then we can’t guarantee that P is nonempty So we should specify A is non empty

[@JasonOvalles]

I don't think you can have a relation defined on the empty set. I mean, reflexivity requires you to have at least one element in A. You couldn't even meet the first criterion for an equivalence relation...

[@TedHopp]

There is no requirement that P be non-empty, only that every element of P be a non-empty subset of A. That requirement is satisfied vacuously if P is empty, and, indeed, the only partition of the empty set is the empty set.

[@Happy_Abe]

@@TedHopp that makes sense thanks

[@martinsangelo3982]

I would like to share a matter of geometric probability Three friends set up a meeting in front of the Nilton Santos stadium to watch a a soccer match. They agreed that each one should arrive in a moment chosen between 3 p.m. and 4 p.m. and that none of them will wait more than 30 minutes for too much, within the stipulated time. What is the probability that the three friends will meet between 3 p.m. and 4 p.m.? Answer : 1/2

[@martinsangelo3982]

Help ?

[@nikolatesla6662]

First view 😁

[@InTheBeginningTheUniverseWas]

third. lol